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Modeling Speech Acts and Joint Intentions in Modal Markov Logic

Modeling Speech Acts and Joint Intentions in Modal Markov Logic. Henry Kautz University of Washington. Goal. Unified way to specify and reason about Communicative actions Domain specific actions Joint and individual obligations Beliefs of agents about other agents Criteria

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Modeling Speech Acts and Joint Intentions in Modal Markov Logic

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  1. Modeling Speech Acts and Joint Intentions in Modal Markov Logic Henry Kautz University of Washington

  2. Goal • Unified way to specify and reason about • Communicative actions • Domain specific actions • Joint and individual obligations • Beliefs of agents about other agents • Criteria • Handle uncertain and incomplete knowledge • Support well-founded and efficient inference • Support learning

  3. Markov Logic • Language for statistical-relational learning • Developed by Pedro Domingos [2004+] • Clausal (CNF) syntax • Clauses may be hard or soft • Weights of soft clauses are learned from examples • Semantics: compilation to a Markov model

  4. Example

  5. Advantages of Markov Logic • Expressive power of (finite domain) first-order logic • Ontologies: project_review(x) => meeting(x) • Relations: manages(Bill,CALO) • Rules:manages(x,y) & DARPA_project(y) => has_headache(x) • Dynamic worlds: at(A,L1,i) & go(L1,L2,i,j) => at(A,L2,j) • Supports both weight and structure learning • Very efficient local-search algorithms for computing most likely assignment (MPE) • Language of CALO Probabilistic Consistency Engine (Uribe & Dietterich)

  6. What’s Missing? • Consider representing the felicity conditions for the speech act Ask_If(S,H,P): • Preconditions: • Speaker does not know whether P holds • Speaker wants to know whether P holds • Speaker believes Hearer knows whether P holds • Effects • Hearer believes Speaker wants to know whether P holds

  7. Modal Logic • Logics for representing attitudes such as Knows, Believes, Wants, Ought, … • Traditionally formalized by rules & axiom schemas, e.g.: • If p can be deduced, then Bp (necessitation) • B(p => q) => (Bp => Bq) (distribution) • Bp => BBp (introspection) • …

  8. Issues in Adding Modalities to Markov Logic • ML is not a deductive system: consequences follow from probabilistic semantics • There cannot be an explicit rule of necessitation; instead, must follow from probabilistic semantics • ML only defined for finite structures • Distribution (and other axiom schemas) must not require infinite instantiations

  9. Modal Markov Logic Ba • Ba P means agent a believes P • Need not be certain belief • Intuitively: the agent’s belief is actionable • Syntax • KB = conjunction of weighted clauses • Clause = disjunction of literals • Literal = Atom or ~Atom • Atom = Proposition or Ba(Clause) • Extend to quantification over sets of constant terms

  10. Inference • Given a KB and a query, construct a Markov graph with • Nodes for each (ground) atom and its negation • Weighted hyperedges for each top-level clause • Unweighted (strict) hyperedges connecting each modal atom to the atoms for its disjuncts, and to the negations of its disjuncts • Enforce consistency • Enforce distribution

  11. Example ~B~p v ~Bp ~B~q v ~Bq B ~p B p B q B ~q B~p & B(p v q) => Bq B~q & B(p v q) => Bp B(p v q)

  12. Uses of soft rules: speech acts • Practically all preconditions and effects of communication acts are non-categorical • E.g.: you may ask a question whose answer you already know the answer • Exceptions (and exceptions to exceptions…) need not be explicitly written into each rule • Higher-weighted rules can over-rule lower weighted rules • Can learn weights (& rules!) corresponding to different styles of discourse

  13. Uses of soft rules: joint obligations • Let M(a,b,g,i) = at time i, agent a is obliged to agent b to perform g • Simple soft persistence axiom: • M(a,b,g,i) => does(a,g) v M(a,b,g,i+1) • A purely logical persistence rule for obligations would be extremely complex • Such complexities (what if b dies? what is g becomes impossible? etc) can be added as needed as additional soft rules

  14. Uses of soft rules: plan recognition & cooperative behavior • Let W(a,p) = agent a wants p • Cooperative agents • Try to recognize the goals of other agents W(a,p) & enables(p,q) => W(a,q) • Adopt those goals as their own (under proper circumstances) B(a,W(b,g)) & cooperative(a,b) => W(a,g)

  15. Status • 2nd generation (non-modal) UW Markov Logic engine has been released • Working on proofs of soundness & completeness of modal extension • Next steps • Implement Markov graph instantiation routines for modalities • Hand-code speech act, obligation persistence, and (simple) plan-recognition rules • Create or find annotated discourse transcripts and use to train weights • Extend SRI/ICSI annotated corpus to include annotations about agents’ mental state, as well as dialogs acts

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